An Old Friend

History CANNOT be changed. Any time you try to change history, it will turn out you were supposed to make that change all along.

This model, assuming it allows an individual to travel back in time to their own past light cone, allows individuals to interfere with their own past and thus necessarily includes some level of predestination paradox. For example: somebody comes from the future and tells you to get into the time machine. You get into the time machine. You go back to the past. You tell your past self to get into the time machine. It is also entirely possible for universes employing this model to include causal loops: ideas and objects which have no origin point.
The majority of stories involving time travel make use of this very simple model. The major difference within stories is in how the universe resists changes to the timeline. For example, if you go back in time and try to kill Hitler or your own grandfather, something, somehow, will stop you. But how? There are four ways I can think of, four sub-models of time travel:The timeline is preserved through dumb luck

This is a favourite; it's used with varying degrees of seriousness in Twelve Monkeys, Futurama, Timeline and The Hitch-Hiker's Guide To The Galaxy.The timeline is actively protected by an intelligence of some kind

The degree of interaction can vary here. We can have anything from human intelligences who send things or people back in time because historical records SAY that was what happened (Bill & Ted's Excellent Adventure, The Terminator) to (occasionally cosmic) police forces which actually have to go back in time after rogue time travellers to stop them from wrecking the timeline (DC comic book universe, Doctor Who).
But in some cases it's dangerous to put certain works of fiction under the heading of "history can never be changed" just because history never IS changed. Just because a timeline is always preserved doesn't mean that it's impossible for the timeline to be altered.
Indeed, if it really was impossible to change history, such active preservation would be completely unnecessary!The timeline is preserved by quantum

Another possibility is detailed in Stephen Baxter's book "Time", in which it seems that time travel involves the sending back and forth through time of quantum packets of information, which alter history multiple times in a kind of feedback loop until the universe settles into a stable structure in which the instance of time travel is completely internally consistent.Time travel isn't always possible

Alternatively, one may have a universe which only allows time travel at certain instants in time and space and only allows a single certain object to travel through time at each instant. This means a time machine will only work at predetermined points in time and will be completely non-functional the rest of the time, or if the wrong thing is in the machine.
In this case the universe is kind of like an office building with time being height, and a finite number elevator shafts leading between certain floors symbolising individual instances of time travel. You can't go back in time unless it's predetermined that you will, and everything will work out fine: if you try, you'll fail.
This model is approximately used in Time Bandits. This is a recognised possible variant on every valid time travel model; for example, it may be that there are no time travellers around us because nobody has built a "receiving station" to accept an incoming time traveller from the future yet, or because there is a blockade across spacetime at some future point in time, across which time travellers are simply unable to pass.